Tentamen (uitwerkingen)

Essential Mathematics for Economic Analysis 6th edition

0 keer verkocht

Vak
Essential Mathematics for Economic Analysis

Instelling
Essential Mathematics For Economic Analysis

Essential Mathematics for Economic Analysis 6th edition Knut Sydsæter Peter Hammond Andr´es Carvajal Arne Strøm Student’s Manual Contents 1 Essentials of Logic and Set Theory 1 2 Algebra 2 3 Solving Equations 9 4 Functions of One Variable 13 5 Properties o...

[Meer zien]

Voorbeeld 4 van de 103 pagina's

Bekijk voorbeeld

Geupload op 13 augustus 2024
Aantal pagina's 103
Geschreven in 2024/2025
Type Tentamen (uitwerkingen)
Bevat Vragen en antwoorden

essential mathematics for economic analysis
essential mathematics for economic analysis 6th ed

Instelling Essential Mathematics for Economic Analysis
Vak Essential Mathematics for Economic Analysis

Volgen

Nurslink

Lid sinds 1 jaar 134 documenten verkocht

€19,61

In winkelwagen

Op verlanglijstje

100% tevredenheidsgarantie
Direct beschikbaar na je betaling
Lees online óf als PDF
Geen vaste maandelijkse kosten

lOMoAR cPSD| 27435123

, lOMoAR cPSD| 27435123

Student’s Manual

Essential Mathematics for
Economic Analysis
6th edition

Knut Sydsæter
Peter Hammond
Andrés Carvajal
Arne Strøm

Student’s Manual

, lOMoAR cPSD| 27435123

Contents

1 Essentials of Logic and Set Theory 1
2 Algebra 2
3 Solving Equations 9
4 Functions of One Variable 13
5 Properties of Functions 17
6 Differentiation 19
7 Derivatives in Use 24
8 Concave and Convex Functions 30
9 Optimization 30
10 Integration 34
11 Topics in Finance and Dynamics 42
12 Matrix Algebra 45
13 Determinants, inverses, and Quadratic Forms 49
14 Functions of Many Variables 61
15 Partial Derivatives in Use 63
16 Multiple Integrals 71
17 Unconstrained Optimization 72
18 Equality Constraints 80
19 Linear Programming 89
20 Nonlinear Programming 94

, lOMoAR cPSD| 27435123

1 Essentials of Logic and Set Theory

1.1 Essentials of Set Theory
1.1.9 For this problem we assume that all the relevant sets are subsets of some “universal” set U . Though
the answer given in the text is fairly complete, we use more words in the answer presented here. As in
S book, let {Ai : i ∈ I} denote the family
the answer in the T of sets, indexed by the set I of labels i. Their
union is A∪ = A , and their intersection is A∩ = A.
i∈I i i∈I i

(a) An element x that belongs to the complement of A∪ cannot belong to any of the sets Ai, so it
/ Ai , for all i in I. It followsTthat for every i in I, x is in the complement Aci = U \ Ai of
satisﬁes x ∈
c
Ai. Thus x belongs to the intersection i∈I Ai of all the sets’ complements.
T
Conversely, if x belongs to the intersection i∈I Aci of all the sets’ complements, then x ∈ / Ai for
/ A , that is, x ∈ (A )c .
all i in I. Then there is no i in I such that x ∈ Ai , which implies that x ∈ ∪ ∪
T
(b) If x belongs to the complement of A∩ = A , then there must be an i in I such that x is not in
c i∈I i
Ai. Then x belongs to the complement A = U \ Ai of Ai. It follows that x must belong to the
S
i
union of all such complements, that is, x ∈ i∈I Aic .
Conversely, if x belongsc the union of all the complements Aic, then for at least one i in I, the
element x belongs to Ai = U \ Ai , that is, x ∈ / Ai . Then x cannot belong to the intersection
∩ T T c
A = i∈I Ai, so x∈( i∈I Ai) .

1.2 Essentials of Logic
1.2.5 (a) If it is false that x ≥ 0 and y ≥ 0, then either x ≥ 0 is false or y ≥ 0 is false (or both), implying that
either x < 0 or y < 0.
Conversely, if either x < 0 or y < 0, then either x ≥ 0 is false or y ≥ 0 is false, so it cannot be true that
both x ≥ 0 and y ≥ 0.
(b) If it is false that all x satisfy x ≥ a, then there exists x such that x < a.
Conversely, if there exists x such that x < a, then it is false that all x satisfy x ≥ a.
(c) If it is false that neither x nor y is less than 5, then it is false that both x ≥ 5 and y ≥ 5, so either
x < 5, or y < 5, or both.
Conversely, if either x < 5, or y < 5, or both, then it is false that both x ≥ 5 and y ≥ 5, so it is false
that neither x nor y is less than 5.
(d) Suppose it is false that for each ε > 0, there exists a δ > 0 such that B is satisﬁed. Then there
exists an ε > 0 such that there is no δ > 0 such that B is satisﬁed. So there exists an ε > 0 such that
B is not satisﬁed for any δ > 0.
Conversely, suppose there exists an ε > 0 such that B is not satisﬁed for any δ > 0. Then is false that,
for each ε > 0, there exists a δ > 0 such that B is satisﬁed.
(e) Suppose it is false that no one can help liking cats. Then there exists someone who can resist liking
cats. (Perhaps it is someone with a severe cat allergy.)
Conversely, suppose someone can resist liking cats. Then it is false that no one can help liking cats.

1

Dit zijn jouw voordelen als je samenvattingen koopt bij Stuvia:

Bewezen kwaliteit door reviews

Studenten hebben al meer dan 850.000 samenvattingen beoordeeld. Zo weet jij zeker dat je de beste keuze maakt!

In een paar klikken geregeld

Geen gedoe — betaal gewoon eenmalig met iDeal, Bancontact of creditcard en je bent klaar. Geen abonnement nodig.

Focus op de essentie

Studenten maken samenvattingen voor studenten. Dat betekent: actuele inhoud waar jij écht wat aan hebt. Geen overbodige details!

Veelgestelde vragen

Wat krijg ik als ik dit document koop?

Je krijgt een PDF, die direct beschikbaar is na je aankoop. Het gekochte document is altijd, overal en oneindig toegankelijk via je profiel.

Tevredenheidsgarantie: hoe werkt dat?

Onze tevredenheidsgarantie zorgt ervoor dat je altijd een studiedocument vindt dat goed bij je past. Je vult een formulier in en onze klantenservice regelt de rest.

Van wie koop ik deze samenvatting?

Stuvia is een marktplaats, je koop dit document dus niet van ons, maar van verkoper Nurslink. Stuvia faciliteert de betaling aan de verkoper.

Zit ik meteen vast aan een abonnement?

Nee, je koopt alleen deze samenvatting voor €19,61. Je zit daarna nergens aan vast.

Is Stuvia te vertrouwen?

4,6 sterren op Google & Trustpilot (+1000 reviews)

Afgelopen 30 dagen zijn er 69052 samenvattingen verkocht

Opgericht in 2010, al 15 jaar dé plek om samenvattingen te kopen

Start met verkopen

Tentamen (uitwerkingen)

Essential Mathematics for Economic Analysis 6th edition

Document informatie

Onderwerpen

Geschreven voor

Verkoper

Ontvangen beoordelingen

Voorbeeld van de inhoud